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Pharmacokinetics from a dynamical systems point of view

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References

  1. A. Garfinkel. A mathematics for physiology.Am. J. Physiol. 245:R455-R466 (1983).

    CAS  PubMed  Google Scholar 

  2. J. J. d'Azzo and C. H. Houpis.Linear Control System Analysis and Design, 3rd ed., McGraw Hill, New York, 1981.

    Google Scholar 

  3. J. P. Crutchfield, J. D. Farmer, N. H. Packard, and R. S. Shaw. Chaos.Sci. Am. 255:38–49 (1986).

    Google Scholar 

  4. R. G. Harrison and D. J. Biswas. Chaos in light. Nature321:394–401 (1986).

    Article  Google Scholar 

  5. E. Ott. Strange attractors and chaotic motions of dynamical systems.Rev. Mod. Phys. 53:655 (1981).

    Article  Google Scholar 

  6. H. G. Schuster.Deterministic Chaos. Physik Verlag Weinheim, FRG, 1984.

    Google Scholar 

  7. R. H. Abraham and C. D. Shaw.Dynamics. The Geometry of Behavior, Pt. 2:Chaotic Behavior, Aerial Press, Santa Cruz, Ca, 1984.

    Google Scholar 

  8. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw. Geometry from a time series.Phys. Rev. Lett. 45:712–716 (1980).

    Article  Google Scholar 

  9. C. Nicolis and G. Nicolis. Is there a climatic attractor?Nature 311:529–532 (1984).

    Article  Google Scholar 

  10. P. Grassberger. Do climatic attractors exist?Nature 323:609–611 (1985).

    Article  Google Scholar 

  11. J. L. Stephenson. Theory of transport in linear biological systems.Bull. Math. Biophys. 22:131–138 (1960).

    Google Scholar 

  12. K. L. Zierler. Theoretical basis of indicator-dilution methods for measuring flow and volume.Circ. Res. 10:393–407 (1962).

    Article  Google Scholar 

  13. J. B. Bassingthwaighte. Blood flow and diffusion through mammalian organs.Science 167:1347–1353 (1970).

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  14. C. Waterhouse and J. Keilson. Transfer times across the human body.Bull. Math. Biophys. 34:33–44 (1972).

    Article  CAS  PubMed  Google Scholar 

  15. R. V. Churchill.Operational Mathematics. McGraw Hill, Kogakusha, Tokyo, 1972.

    Google Scholar 

  16. A. Papoulis.Probability, Random Variables and Stochastic Processes, McGraw Hill, Kogakusha, Tokyo, 1965.

    Google Scholar 

  17. K. Yamaoka, T. Nakagawa, and T. Uno. Statistical moments in pharmacokinetics.J. Pharmacokin. Biopharm. 6:547–558 (1978).

    Article  CAS  Google Scholar 

  18. S. Grodins.Control Theory and Biological Systems, Columbia University Press, New York, 1963.

    Google Scholar 

  19. N. A. Lassen and W. Perl.Tracer Kinetic Methods in Medical Physiology, Raven Press, New York, 1979.

    Google Scholar 

  20. J. J. Di Stefano, A. R. Stubberub, and I. J. Williams.Feedback and Control Systems, McGraw Hill, New York, 1976.

    Google Scholar 

  21. H. T. Milhorn.The Application of Control Theory to Physiological Systems, W. B. Saunders, Philadelphia, 1966.

    Google Scholar 

  22. D. P. Vaughan and I. Hope. Applications of a recirculatory stochastic pharmacokinetic model: Limitations of compartmental models.J. Pharmacokin. Biopharm. 7:207–225 (1979).

    Article  CAS  Google Scholar 

  23. D. J. Cutler. A linear recirculation model for drug disposition,J. Pharmacokin. Biopharm. 7:101–116 (1979).

    Article  CAS  Google Scholar 

  24. J. M. van Rossum, J. Burgers, G. van Lingen, and J. de Bie. Pharmacokinetics: A dynamic systems approach.TIPS, January, 1983.

  25. M. Weiss and W. Föster. Pharmacokinetic models based on circulatory transport.Eur. J. Clin. Pharmacol. 16:287–297 (1979).

    Article  Google Scholar 

  26. K. Yamaoka, T. Nakagawa, and H. Tanaka. Recirculatory moment analysis of drugs in man.Chem. Pharm. Bull. 33:784–794 (1985).

    Article  CAS  PubMed  Google Scholar 

  27. M. Weiss. Modelling of initial distribution of drugs following intravenous bolus injection.Eur. J. Clin. Pharmacol. 24: 121–126 (1983).

    Article  CAS  PubMed  Google Scholar 

  28. J. M. van Rossum, O. Steyger, T. van Uem, G. J. Binkhorst, and R. A. A. Maes. Pharmacokinetics by using mathematical systems dynamics. In J. Eisenfeld and M. Witten (eds.),Modelling of Biomedical Systems, Elsevier, Amsterdam 1986, pp. 121–126.

    Google Scholar 

  29. J. M. van Rossum, G. van Lingen, and R. A. A. Maes. Analysis of the pharmacokinetic body transport function.Math. Comput. Model. 11:610–614 (1988).

    Article  Google Scholar 

  30. H. W. A. Teeuwen, P. J. de Schepper, T. B. Tjandramaga, A. van Hecken, R. Veldhuis, and J. M. van Rossum. Intravenous single dose pharmacokinetics of caffeine.Eur. J. Clin. Pharmacol. (in press).

  31. H. W. A. Teeuwen, T. B. Tjandramaga, A. van Hecken, and J. M. van Rossum. Clinical pharmacokinetics of paraxanthine.Eur. J. Clin. Pharmacol. (in press).

  32. H. W. A. Teeuwen, A. van Hecken, T. B. Tjandramaga, and J. M. van Rossum. Oral and single dose kinetics of quinine.Eur. J. Clin. Pharmacol. (in press).

  33. D. P. Vaughan and M. Dennis. Mathematical basis of point-area deconvolution method for determining in vivo input functions,J. Pharm. Sci. 67:663–665.

  34. S. Øle, J. G. Gambertoglio, and L. Fleckenstein. Comparison of the disposition of total and unbound sulfisoxazole after single and multiple dosing.J. Pharmacokin. Biopharm. 10:157–172 (1982).

    Article  Google Scholar 

  35. J. Raaflaub and U. C. Dubach. On the pharmacokinetics of phenacetin in man.Eur. J. Clin. Pharmacol. 8:261–265 (1975).

    Article  CAS  PubMed  Google Scholar 

  36. M. D. Rawlins, D. B. Henderson, and A. R. Hijab. Pharmacokinetics of paracetamol (acetaminophen) after intravenous and oral administration.Eur. J. Clin. Pharmacol. 11:283–286 (1977).

    Article  CAS  PubMed  Google Scholar 

  37. M. Eichelbaum, H. R. Ochs, G. Roberts, and A. Somogyi. Pharmacokinetics and metabolism of antipyrine (phenazone) after intravenous and oral administration.Arzneim.-Forsch. 32:575–578 (1982).

    CAS  Google Scholar 

  38. U. Breyer-Pfaff, M. Harder, and E. H. Egberts. Plasma levels of parent drug and metabolites in the intravenous aminopyrine breath test.Eur. J. Clin. Pharmacol. 21:521–528 (1982).

    Article  CAS  PubMed  Google Scholar 

  39. P. A. Mitenko and R. I. Ogilvie. Pharmacokinetics of intravenous theophylline.Clin. Pharmacol. Ther. 14:509–513 (1973).

    CAS  PubMed  Google Scholar 

  40. N. L. Benowitz, P. Jacob, R. T. Jones, and J. Rosenberg. Interindividual variability in the metabolism and cardiovascular effects of nicotine in man.J. Pharmacol. Exp. Ther. 221:368 (1982).

    CAS  PubMed  Google Scholar 

  41. P. J. de Schepper, A. van Hecken, P. Daenens, and J. M. van Rossum. Kinetics of cotinine after oral and intravenous administration in man (in preparation).

  42. S. M. Huang, N. K. Alhanikan, K. Sridhar, Y. C. Huang, and W. L. Chiou. Pharmacokinetics of chlorpheniramine after intravenous and oral administration in normal adults.Eur. J. Clin. Pharmacol. 22:359–365 (1982).

    Article  CAS  PubMed  Google Scholar 

  43. R. Jochemsen, J. J. H. Hogendoorn, J. Dingemanse, J. Hermans, J. K. Boeijinga, and D. D. Breimer. Pharmacokinetics and bioavailability of intravenous, oral, and rectal nitrazepam in humans.J. Pharmacokin. Biopharm. 10:231–245 (1982).

    Article  CAS  Google Scholar 

  44. U. Klotz and G. Ziegler. Physiologic and temporal variation in hepatic elimination of midazolam.Clin. Pharmacol. Ther. 32:107–112 (1982).

    Article  CAS  PubMed  Google Scholar 

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van Rossum, J.M., de Bie, J.E.G.M., van Lingen, G. et al. Pharmacokinetics from a dynamical systems point of view. Journal of Pharmacokinetics and Biopharmaceutics 17, 365–392 (1989). https://doi.org/10.1007/BF01061902

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